\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{nickknack04}
\pdfinfo{
  /Title (semiconductors.pdf)
  /Creator (Cheatography)
  /Author (nickknack04)
  /Subject (Semiconductors Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{9EB7DE}
\definecolor{LightBackground}{HTML}{F2F6FA}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Semiconductors Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{nickknack04} via \textcolor{DarkBackground}{\uline{cheatography.com/207653/cs/44399/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}nickknack04 \\
  \uline{cheatography.com/nickknack04} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 18th September, 2024.\\
   Updated 18th September, 2024.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Voltage Amplifier}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{V\textasciitilde{}i\textasciitilde{} = V\textasciitilde{}s\textasciitilde{} * (R\textasciitilde{}i\textasciitilde{} / (R\textasciitilde{}i\textasciitilde{} + R\textasciitilde{}s\textasciitilde{}))} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{V\textasciitilde{}o\textasciitilde{} = A\textasciitilde{}vo\textasciitilde{}V\textasciitilde{}i\textasciitilde{} * (R\textasciitilde{}L\textasciitilde{} / (R\textasciitilde{}L\textasciitilde{} + R\textasciitilde{}o\textasciitilde{}))} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Ideal op-amp:}} \{\{nl\}\} R\textasciitilde{}i\textasciitilde{} = infinity\{\{nl\}\} R\textasciitilde{}o\textasciitilde{} = 0 \{\{nl\}\} R\textasciitilde{}L\textasciitilde{} = R\textasciitilde{}s\textasciitilde{} = 0 affect on gain} \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Four Amplifier Models}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Voltage Amplifier}} & {\bf{Current Amplifier}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
A\textasciitilde{}v\textasciitilde{} = V\textasciitilde{}o\textasciitilde{} / V\textasciitilde{}i\textasciitilde{} \{\{nl\}\} R\textasciitilde{}i\textasciitilde{} = infinity\{\{nl\}\}R\textasciitilde{}o\textasciitilde{} = 0 & A\textasciitilde{}v\textasciitilde{} = i\textasciitilde{}o\textasciitilde{} / i\textasciitilde{}i\textasciitilde{} \{\{nl\}\} R\textasciitilde{}i\textasciitilde{} = 0\{\{nl\}\}R\textasciitilde{}o\textasciitilde{} = infinity \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
{\bf{Transconductance Amp}} & {\bf{Transresistance Amp}} \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
G\textasciitilde{}m\textasciitilde{} (i dep.) = i\textasciitilde{}o\textasciitilde{} / V\textasciitilde{}i\textasciitilde{} \{\{nl\}\} R\textasciitilde{}i\textasciitilde{} = infinity\{\{nl\}\}R\textasciitilde{}o\textasciitilde{} = infinity & R\textasciitilde{}m\textasciitilde{} (v dep.) = V\textasciitilde{}o\textasciitilde{} / i\textasciitilde{}i\textasciitilde{} \{\{nl\}\} R\textasciitilde{}i\textasciitilde{} = 0\{\{nl\}\}R\textasciitilde{}o\textasciitilde{} = 0 \tn 
% Row Count 11 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Source Transformation}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{A\textasciitilde{}vo\textasciitilde{} = A\textasciitilde{}is\textasciitilde{} * (R\textasciitilde{}o\textasciitilde{} / R\textasciitilde{}i\textasciitilde{}) = G\textasciitilde{}m\textasciitilde{} * R\textasciitilde{}o\textasciitilde{} = R\textasciitilde{}m\textasciitilde{} / R\textasciitilde{}i\textasciitilde{}% Row Count 2 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Inverting vs. Non-Inverting Op-Amp}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Inverting Op-Amp}} \{\{nl\}\}A\textasciitilde{}v\textasciitilde{} = R\textasciitilde{}f\textasciitilde{} / R\textasciitilde{}i\textasciitilde{} & {\bf{Non-Inverting Op-Amp}} \{\{nl\}\} A\textasciitilde{}v\textasciitilde{} = 1 + R\textasciitilde{}f\textasciitilde{} / R\textasciitilde{}i\textasciitilde{} \tn 
% Row Count 3 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Astable Multivibrator}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/nickknack04_1726672448_Screenshot 2024-09-18 111217.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{τ = CR \newline T = 2τ * ln{[}(1 + β) / (1 - β){]} \newline β = R\textasciitilde{}1\textasciitilde{} / (R\textasciitilde{}1\textasciitilde{} + R\textasciitilde{}2\textasciitilde{})}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Gain in dB}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{A\textasciitilde{}v\textasciitilde{} = 20log|A\textasciitilde{}v\textasciitilde{}| dB} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{A\textasciitilde{}i\textasciitilde{} = 20log|A\textasciitilde{}i\textasciitilde{}| dB} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{P\textasciitilde{}g\textasciitilde{} = 10log|P\textasciitilde{}g\textasciitilde{}| dB} \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Differential Amplifier (CMRR)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{20log|A\textasciitilde{}d\textasciitilde{} / A\textasciitilde{}cm\textasciitilde{}| = 20log|(K+1) / {\bf{δ}}| = 20log|(K+1) / (4*{\bf{ε}})| \newline % Row Count 2 (+ 2)
{\bf{δ}} = mismatch \newline % Row Count 3 (+ 1)
{\bf{ε}} = tolerance \newline % Row Count 4 (+ 1)
A\textasciitilde{}d\textasciitilde{} = R\textasciitilde{}2\textasciitilde{} / R\textasciitilde{}1\textasciitilde{} = R\textasciitilde{}4\textasciitilde{} / R\textasciitilde{}3\textasciitilde{} = {\bf{K}} \newline % Row Count 5 (+ 1)
V\textasciitilde{}cmi\textasciitilde{} = 0.5(V\textasciitilde{}1\textasciitilde{} + V\textasciitilde{}2\textasciitilde{}) \{\{nl\}\}V\textasciitilde{}1\textasciitilde{} = V\textasciitilde{}cmi\textasciitilde{} - 0.5V\textasciitilde{}di\textasciitilde{}\{\{nl\}\}V\textasciitilde{}2\textasciitilde{} = V\textasciitilde{}cmi\textasciitilde{} + 0.5V\textasciitilde{}di\textasciitilde{}% Row Count 7 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{555 Timer (Monostable)}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/nickknack04_1726672601_Screenshot 2024-09-18 111526.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{T = CR * ln3 \textasciitilde{}= 1.1CR \newline V\textasciitilde{}TH\textasciitilde{} = V\textasciitilde{}cc\textasciitilde{}(1 - e\textasciicircum{}T/CR\textasciicircum{})}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Amplifier Class}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{A: Full wave, θ\textasciitilde{}c\textasciitilde{} = 360 deg.} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{B: Halfwave θ\textasciitilde{}c\textasciitilde{} = 180 deg.} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{C: Between A \& B class, θ\textasciitilde{}c\textasciitilde{} \textless{} 180 deg.} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{D: Small wave} \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Bistable Multivibrator}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/nickknack04_1726672247_Screenshot 2024-09-18 110753.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{β = R\textasciitilde{}1\textasciitilde{} / (R\textasciitilde{}1\textasciitilde{} + R\textasciitilde{}2\textasciitilde{}) \newline {\bf{V\textasciitilde{}TH\textasciitilde{} - V\textasciitilde{}TL\textasciitilde{} = β(L\textasciitilde{}+\textasciitilde{} - L\textasciitilde{}-\textasciitilde{})}} \newline  \newline V\textasciitilde{}TL\textasciitilde{} = -L\textasciitilde{}+\textasciitilde{} (R\textasciitilde{}1\textasciitilde{} / R\textasciitilde{}2\textasciitilde{}) \newline V\textasciitilde{}TL\textasciitilde{} = -L\textasciitilde{}-\textasciitilde{} (R\textasciitilde{}1\textasciitilde{} / R\textasciitilde{}2\textasciitilde{})}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{555 Timer (Astable)}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/nickknack04_1726673296_BRUH.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Duty Cycle = (R\textasciitilde{}A\textasciitilde{} + R\textasciitilde{}B\textasciitilde{}) / (R\textasciitilde{}A\textasciitilde{} + 2R\textasciitilde{}B\textasciitilde{}) \newline T = 0.69C(R\textasciitilde{}A\textasciitilde{} + 2R\textasciitilde{}B\textasciitilde{})}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}